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Evaluate lim(xtooo) (sqrt(x^(2)+1)-root(...

Evaluate `lim_(xtooo) (sqrt(x^(2)+1)-root(3)(x^3+1))/(root(4)(x^(4)+1)-root(5)(x^(4)+1))`

Text Solution

Verified by Experts

We have `underset(xtooo)lim(sqrt(x^(2)+1)-root(3)(x)+1)/(root(4)(x^(4)+1)-1root(5)(x^(4)+1))`
`underset(xtooo)lim(sqrt(1+(1)/(x^(4)))-root(3)(1+(1)/(x^(3))))/(root(4)(1+(1)/(x^(4)))-root(5)((1)/(x)+(1)/x^(5)))=(1-1)/(1-0)=0`
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